Lay out the toasted bread on each of four serving plates. Divide the mayonnaise among the 4 bread slices and spread evenly. Toss the arugula, red onion, and vinegar in a bowl, seasoning to taste with salt and pepper.

Top each slice of bread with the arugula mixture. Top with a thin slice of smoked salmon. Top each sandwich with 1 hard cooked egg, shingling or fanning out the slices to cover the sandwich. Enjoy!